Prethermalization and dynamic phase transition in an isolated trapped ion spin chain

We propose an experimental scheme to observe prethermalization and a dynamic phase transition in a one-dimensional XY spin chain with long-range interactions and inhomogeneous lattice spacing, which can be readily implemented with a recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at an intermediate timescale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is shown to result from a non-trivial structure in the lower half of the energy spectrum. The dynamic behavior of the system is shown to cross different phases when the interaction range is continuously tuned, indicating the existence of a dynamic phase transition.